P.G. de Gennes, Scaling Concepts in Polymer Physics. Cornell Univ. Press, Ithaca (1979).  Home/Search   Document Not in Database   Summary   Related Articles   Check

....polymer becomes adsorbed onto the surface [5] For high temperatures, T T a ) the polymer is in a desorbed phase where it extends a large distance into the solvent above the surface to which it is attached. For low temperatures, T T a ) the polymer is in an adsorbed phase. It is well known [6] that there is a correspondence between SAWs and the O(n) model in the limit n 0. The O(n) model has been considered with three different boundary conditions: free boundary spins, where the bulk and surface couplings are the same; fixed boundary spins; and critically enhanced surface coupling ....

de Gennes P. G., Scaling concepts in polymer physics, (Cornell University) 1979.

....have been explored, such as genetic algorithms in the seminal work of Unger and Moult [21] In this paper we demonstrate the e#ectiveness of pull moves, a new local move set, with a tabu search algorithm on the 2D HP problem. The pull moves we define recall the classic de Gennes reptation model [6, 7] for polymer motion. In our experiments, pull moves appear quite effective, they may be useful in conjunction with other local search techniques that have been applied to the problem. As a theoretical contribution, we prove that pull moves are complete, i.e. any valid configuration can be ....

P. G. de Gennes. Scaling Concepts in Polymer Physics. Cornell University Press, 1979.

....phase transitions. Self avoiding walks, polygons and polyominoes arise, for example, in models of polymers, of cell growth, of percolation. Moreover, the self avoiding walk problem is equivalent to the resolution of the limit n 0 of the n vector model, which generalizes the famous Ising model [8]. Finally, a quite important example is the correspondence between the enumeration of directed polyominoes on a regular lattice in dimension D and the resolution of a gas model in dimension D Gamma 1 [13] Despite serious efforts over the last 40 years, these problems are completely open. ....

P.-G. de Gennes, Scaling concepts in polymers physics, Cornell University Press (1979).

....part by NSF CAREER Grant CCR 9983832 and an Alfred P. Sloan Research Fellowship. This work was done while visiting Mitsubishi Electric Research Laboratories. ISupported in part by NSERC and FCAR. This work was done in part while visiting Mitsubishi Electric Research Laboratories. reptation model [6, 7] for polymer motion. t In our experiments, pull moves appear quite effective, they may be useful in conjunction with other local search techniques that have been applied to the problem. As a theoretical contribution, we prove that pull moves are complete, i.e. any valid configuration can be ....

P. G. de Gennes. Scaling Concepts in Polymer Physics. Cornell University Press, 1979.

....in [23] for the lamellar phase of diblock copolymers. 2 The free energy functional The order parameter model we use was derived in Ren and Wei [22] Suppose that in a triblock copolymer molecule there are NA many type A, NB many type B, and NC many type C monomers. The Kuhn statistical length [7, 12] measures the average length between two adjacent monomers in a chain. We assume that this length is independent of the types of adjacent monomers, and denote it by l. The relative numbers of the three type monomers in every molecule are a = NA N 0; b = NB N 0; c = NC N 0; a b c = ....

....t) 0; 1; 0) t. The function W we use is, according to (2.4) and (2.7) u k um Gamma u k : From these j and W we deduce (1 Gamma t)t dt) 3.14) and similar expressions for e . The constants in e are called the Flory Huggins parameters [7, 12] in polymer science and are defined by = fiV Gamma (fi=2) V V mm ) 0; k 6= m: 3.15) We must assume that the three parameters are all positive. This is because in a block copolymer, dislike monomers repel each other more than like ones do. We point out that our problem depends on ....

P.G. de Gennes. Scaling Concepts in Polymer Physics. Cornell University Press, Ithaca, NY, 1979.

....models. Key words: self avoiding walk, pivot algorithm, polymer. 1 1 Introduction The self avoiding walk (SAW) is a simple model for polymers in dilute solution. The interest in the model extends well beyond this application since the model has critical exponents which exhibit universality [1, 2]. The pivot algorithm provides a fast Monte Carlo algorithm for simulating the model, and so it is an ideal laboratory for studying renormalization group predictions and, in two dimensions, conformal eld theory predictions. This algorithm rst appeared in the literature in 1969 [3] When Madras ....

P.G. de Gennes, Scaling Concepts in Polymer Physics, Cornell Univ. Press, Ithaca, NY, 1979.

....is a long chain of connected monomers, its building molecular units. A flexible polymer in solution has typical dimensions in the range 1 50 nm. When a polymer chain is brought to the neighbourhood of a repulsive, impenetrable wall, the number of conformations available to the chain is reduced [1]. Such a reduction of conformational entropy creates a nonhomogeneous pressure field acting on the wall in a region comparable to the polymer size. As we will now show, the pressure field can be controlled by choosing how the chain approaches the surface but also by tuning the chain size and ....

De Gennes P.-G., Scaling Concepts in Polymers Physics, Cornell University Press, Ithaca, 1979.

.... which always assume some invariance of the system properties under a scaling rule(s) appear to be informative mostly to physicists who, most frequently under the self similarity assumption(s) try to understand quite general static as well as dynamic properties of the system under investigation [4]. Theoretical studies on the kinetics of cluster growth are observed to split up into two main directions: 1) computer simulations: Monte Carlo (MC) cellular automata (CA) as well as molecular dynamics (MD) 2) analytical studies on dynamics or kinetics of some systems with evolving fronts, ....

.... for the evolution of a uctuating di usion reaction front [5] notice that the concept of fractality of any kind is often used for description of the above mentioned phenomena; cf. 1, 6] for general overview; also, a scaling concept, being very useful in polymer physics, is very much advised here [4, 7]. In this study, beginning the whole story with a discrete picture of a selfavoiding polygon embedded in the square lattice (Fig. 1(a) and applying both scaling arguments as well as a Steinhaus rule for evaluating the polygon s area (Fig. 2) we may, by imposing a discrete time dynamics on the ....

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P.G. De Gennes, Scaling Concepts in Polymer Physics, Cornell University Press, Ithaca, New York 1979.

....is equivalent to the Hartree type approximation) was earlier also successfully applied to the investigation of static properties of different models with [10 12] or without [13 15] replica symmetry breaking. The basic description for polymer dynamics in general is the so called Rouse model [16,17], where the polymer configuration is expressed in dynamical modes. The physical background of the Rouse model is very simple: It corresponds to a non interacting chain stirred by a white noise random force, in the usual Langevin sense. It is well known from experiments [18] but also very ....

....usual Langevin sense. It is well known from experiments [18] but also very surprising that this Rouse model provides a good description for the melt of the relatively short chains N N e . At higher degrees of polymerization the dynamics of the long chain can be described by the reptation model [16,17,19]. For the case of the short chain melt, it is not obvious that the collisions of the surrounding chains close to a test chain add up to a white noise force. On the other hand, the obvious thought to explain the Rouseian behavior in short chain polymer melts is first the excluded volume screening ....

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P.G.deGennes, Scaling Concepts in Polymer Physics, Cornell Univ. Press, Ithaca, N.Y., 1979

....the behavior of the system and hence should be used as a parameter to explain experimental results. PACS numbers: 61.25.Hq, 36.20. r, 87.15. v E mail: kremer mpip mainz.mpg.de, holm mpip mainz.mpg.de 1 Author to whom correspondence should be addressed. 1 Introduction Unlike neutral polymers [1, 2, 3], the understanding of the behavior of electrically charged macromolecules, short polyelectrolytes, is still rather poor. The long range nature of the electrostatic interactions introduces new length and time scales that render the analytical description very complicated [4] and prevent simple ....

P. de Gennes, Scaling Concepts in Polymer Physics, Cornell University Press, Ithaca, NY (1979).

....references therein. The standard mathematical introduction to random polymers is [MS93] and good introductory texts covering certain aspects of this subject are [dH96] Sl96] and [Fr81] For an introduction to polymer models from a physicist s or chemist s point of view, see [Fl49] vdZ98] and [dG79]. 1. Weakly self avoiding walk 1.1 Model and motivation. A random polymer is a long chain of smaller molecules which have the tendency to occupy the space nowhere too tightly. The reason for this self repellence is the so called excluded volume e ect: It is energetically favorable to spread out ....

P.G. de Gennes, Scaling Concepts in Polymer Physics, Cornell University Press, Ithaca 1979.

....analysis [6] Among the various approaches, the one making use of scaling concepts has been successful especially for the characterization of financial time series. Scaling concepts provide a unifying and very useful tool for the investigation of phenomena in physics, chemistry and biology [7 9]. The use of scaling concepts in the economic and social sciences can be traced back at least to the work of Zipf [10] who discovered the rank frequency statistics taking now 2 his name. Essentially, Zipf found that the frequency of a word in a written document is inversely proportional to the ....

P.G. De Gennes, Scaling Concepts in Polymer Physics, Cornell University Press, Ithaca, NY, 1979.

....polymeric systems [1] It originates from the presence of an infinite network. On a macroscopic level uncrosslinked polymeric systems exhibit a viscous flow rather than an elastic recovery behavior. However, on a microscopic level a single polymer chain is endowed with an elastic response [2]. This is a combined e#ect of both the chain connectivity and the huge number of possible conformations. Here we examine the elasticity of a single random heteropolymer chain that undergoes a freezing transition. This transition leads to a non ergodic phase characterized by a highly rugged ....

....outside the frozen phase, # # , # =# # , # = 2 d #U # # V . 20) Curly brackets indicate here that #= #. According to eq. 20) above the freezing transition the elastic constants originate from the chain connectivity. Note that this result is applicable to both a homopolymer chain [2] and a heteropolymer chain in the random coil and liquid like phases. In the frozen phase, along with the regular part (20) one has an extra response ## # , # to the external deformation. Such extra response originates in the last term of eq. 17) that we denote as ##(u) Performing n # 0 ....

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de Gennes P. G., Scaling Concepts in Polymer Physics (Cornell University Press, Ithaca) 1989.

....points and exponents are estimated. Walks on several of the patterns appear to belong to the same universality class as walks on the hexagonal periodic lattice. 1 1 Introduction Much is known about the asymptotic properties of random walks on periodic two and three dimensional lattices [1, 2, 3]. In particular, self avoiding walks (in which self intersection is not allowed) have been of particular interest for several reasons: as models of polymers [1, 4] because of their connection with statistical mechanical spin models such as the Potts model [5] and because of the availability of ....

.... 1 1 Introduction Much is known about the asymptotic properties of random walks on periodic two and three dimensional lattices [1, 2, 3] In particular, self avoiding walks (in which self intersection is not allowed) have been of particular interest for several reasons: as models of polymers [1, 4]; because of their connection with statistical mechanical spin models such as the Potts model [5] and because of the availability of some exact results [6] It is natural to ask which of the known properties of lattice walks carry over to the case of quasilattices. A start has been made on this ....

P.-G. de Gennes, Scaling concepts in Polymer physics, Cornell University Press, 1979.

....e.g. dynamic structure factor of light scattering are presented, and again simple applications are discussed. 1 1 Introduction The equilibrium properties of polymers in dilute solution have been studied much in recent years, yielding many interesting insights. There are well founded scaling [1] and statistical mechanical methods [2] that can be applied, and computer simulation has proved to be a particularly powerful tool [3] However, methods that permit us to study dynamics and kinetic phenomena are much less well developed, and the traditional methods of non equilibrium statistical ....

P.G. de Gennes, Scaling Concepts in Polymer Physics. Cornell Univ. Press, Ithaca (1979).

....critical behavior. This crossover occurs, for instance, when the interaction range (and hence the Ginzburg number G entering the Ginzburg criterion [5] is varied [6 12] A closely related crossover is found for symmetrical polymer mixtures when the chain length N of the polymers is varied [4,13 23]. A part of this crossover (though typically not the full extent of the crossover scaling function) can be probed experimentally near the critical point of #uids and #uid binary mixtures [24 27] While the Ginzburg criteria [5,14 16] provide a qualitative understanding of this crossover, the ....

.... the question as to what extent (if at all) such crossover scaling functions are universal is an intriguing one [10 12,24 26,36] Another very interesting crossover which can also be studied is that which occurs near the critical point of unmixing for polymer solutions in a bad solvent [13,37 46]. For chain length N ## the critical temperature T c (N ) moves towards the # temperature, where a single coil undergoes a transition from a swollen coil to a collapsed globule. This limit corresponds to a tricritical point [13] Monte Carlo analyses of critical phenomena typically apply ....

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P.G. de Gennes, Scaling Concepts in Polymer Physics, Cornell University Press, Ithaca, 1979.

....with a nearperiodic arrangement of locally collapsed blobs, which is then believed to coarsen, and we have discussed this phenomenon elsewhere. 1 1 Introduction The equilibrium properties of polymers in dilute solution have been thoroughly studied in recent years using well founded scaling [1] and statistical mechanical methods [2] Although computer simulation of polymer kinetics has proved to be very fruitful [3] analytical techniques that permit us to study dynamics and kinetic phenomena [4] 5] are much less well developed, and the traditional methods of non equilibrium ....

P.G. de Gennes, Scaling Concepts in Polymer Physics. Cornell Univ. Press, Ithaca (1979).

....critical behavior. This crossover occurs, for instance, when the interaction range (and hence the Ginzburg number G entering the Ginzburg criterion [4] is varied [5 11] A closely related crossover is found for symmetrical polymer mixtures when the chain length N of the polymers is varied [3,12 21]. A part of this crossover (though typically not the full extent of the crossover scaling function) can be probed experimentally near the critical point of fluids and fluid binary mixtures [22 24] While the Ginzburg criteria [4,13,14] provide a qualitative understanding of this crossover, the ....

.... particular, the question as to what extent (if at all) such crossover scaling functions are universal is an intriguing one [9 11,22,23,33] Another very interesting crossover which can also be studied is that which occurs near the critical point of unmixing for polymer solutions in a bad solvent [12,34 43]. For chain length N ##the critical temperature T c (N) moves towards the # temperature, where a single coil undergoes a transition from a swollen coil to a collapsed globule. This limit corresponds to a tricritical point [12] Monte Carlo analyses of critical phenomena typically apply ....

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P.G. de Gennes, Scaling Concepts in Polymer Physics (Cornell University Press, Ithaca, 1979).

....of these algorithms are discussed, based on careful tests for a small system. 1 irback thep.lu.se 2 erik thep.lu. se 1 Introduction The thermodynamic behavior of isolated homopolymers is known in quite some detail at and above their collapse temperature T = T , from analytical work [1, 2, 3] and numerical simulations of very long chains [4, 5] Much less is known about the behavior at low temperatures. Consequently, it is of utmost interest to examine the low T phase behavior and its model dependence, which, in particular, may shed light on the mechanism of folding for ....

P.G. de Gennes, Scaling Concepts in Polymer Physics (Cornell University Press, Ithaca, 1988).

....fl Gamma1 (7.1) c N (x) N N ff sing Gamma2 (x fixed 6= 0) 7.2) h 2 N i N 2 (7.3) as N 1; here fl, ff sing and are critical exponents, while (the connective constant of the lattice) is the analogue of a critical temperature. The SAW has direct application in polymer physics [74], and is indirectly relevant to ferromagnetism and quantum field theory by virtue of its equivalence with the n 0 limit of the n vector model [75] The SAW has some advantages over spin systems for Monte Carlo work: Firstly, one can work directly with SAWs on an infinite lattice; there are no ....

P.G. DeGennes, Scaling Concepts in Polymer Physics (Cornell Univ. Press, Ithaca NY, 1979).

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P.G. de Gennes, Scaling Concepts in Polymer Physics. Cornell Univ. Press, Ithaca (1979).

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P.G. de Gennes, Scaling Concepts in Polymer Physics (Cornell Univ. Press, Ithaca, 1979).

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P.G. de Gennes, Scaling Concepts in Polymer Physics (Cornell Univ. Press, Ithaca, 1979).

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P. G. de Gennes, Scaling Concepts in Polymer Physics (Cornell University Press, Ithaca, NY, 1979).

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deGennes, P.-G. (1979). Scaling Concepts in Polymer Physics. Cornell University Press, Ithaca, N.Y.

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