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Thermodynamics of Polymer Mixtures
Published in Timothy P. Lodge, Paul C. Hiemenz, Polymer Chemistry, 2020
Timothy P. Lodge, Paul C. Hiemenz
We now return to this rather tricky problem, armed with enough information to say something useful. In Chapter 6 we examined in detail the mean-square radius of gyration, and the segment distribution function, for flexible chains. As pointed out then, we left out one very important physical feature, namely that a real polymer chain cannot intersect itself. We modeled the chain as a random walk, whereas in reality it is a self-avoiding walk. The current best estimate of the exact result for a self-avoiding walk is Rg ∼ N0.589, but we follow common practice and approximate this relation as Rg ∼ N0.6. The problem of a polymer in solution has another aspect we did not consider in Chapter 6, namely that there will generally be some interaction energy between a polymer segment and a solvent molecule. In an athermal solvent (ΔHm = 0), χ = 0, and there is no energetic price to pay for having a solvent molecule next to a polymer segment. In such a case the full self-avoiding walk statistics apply, and the chain is larger than its unperturbed dimensions described by Equation 6.5.3. Often this coil is said to be “swollen,” and the degree of swelling or “coil expansion” is quantified by the expansion factor, α: α≡RgRg,0
Non-stationary (postpolymerization) polymerization kinetics problems
Published in Yu. G. Medvedevskikh, A.R. Kytsya, L.I. Bazylyak, A.A. Turovsky, G.E. Zaikov, Stationary and Non-Stationary Kinetics of the Photoinitiated Polymerization, 2004
Yu. G. Medvedevskikh, A.R. Kytsya, L.I. Bazylyak, A.A. Turovsky, G.E. Zaikov
Although in the presented kinetic scheme of a process ((4.23)-(4.25) in the interface layer the conception of the control of the chain propagation rate on the rate of its termination is used, here the chain termination is a monomolecular one and represents the radical self-burial act, but not the radical trapping. Such a mechanism is well-known and is discussed in the self-avoiding walks model, which describes the statistics of polymers well. However, direct comparison of the values of obtained constants k11 and k12 with the selfavoiding walks model is complicated: according to this model the probability of a chain surviving is determined by the coordinative number of grating, on which the probability of a free unit location in the nearest environment of occupied with an active center of radical will depend.
Polymer Rheology- Effect of Various Parameters
Published in B. R. Gupta, Rheology Applied in Polymer Processing, 2023
An ideal chain (or freely jointed chain Fig. 4.5) is the simplest model to describe polymers such as nucleic acid and proteins [en.wikipedia.org, edited Feb. 2017]. A random walk is a mathematical object, known as a stochastic or random process, that describes a path that consists of a succession of random steps on some mathematical space such as integers. Self avoiding walk (SAW) is a sequence of moves on a lattice ( a lattice path) that does not visit the same point more than once. The idea of excluded volume refers to the idea that one part of the long chain molecule can not occupy space that is already occupied by another part ofthe same molecule Fig. 4.5 (a) . The excluded volume causes the ends of a polymer chain in a solution to be further apart
Reproduction operators in solving LABS problem using EMAS meta-heuristic with various local optimization techniques
Published in Journal of Information and Telecommunication, 2023
Sylwia Biełaszek, Kamil Piętak, Marek Kisiel-Dorohinicki
There is a lot of various techniques that try to solve the problem. The simplest method of solving LABS is exhaustive enumeration that provides the best results, but can be applied only to small values of L. There are also a lot of various heuristic algorithms that use some plausible rules to locate good sequences more quickly. A well-known method for such techniques is steepest descend local search (SDLS) (Bartholomew-Biggs, 2008) or tabu search (Gallardo et al., 2009). In recent years, a few modern solvers based on the self-avoiding walk concept have been proposed. The most promising solvers are lssOrel (Bošković et al., 2014) and xLostavka (Brest & Bošković, 2018), which are successfully used for finding skew-symmetric sequences of lengths between 301 and 401 (Brest & Bošković, 2020). These techniques can be also parallelized utilizing GPGPU architectures what was shown in Pietak et al. (2019); Żurek et al. (2017).
Public transportation in Great Britain viewed as a complex network
Published in Transportmetrica A: Transport Science, 2019
Robin de Regt, Christian von Ferber, Yurij Holovatch, Mykola Lebovka
The above empirical research has revealed that PTN constructed in cities with different geographical, cultural and historical background share a number of basic common topological properties: they appear to be strongly correlated structures with high values of clustering coefficients and comparatively low mean shortest path values, their node degree distributions are often found to follow exponential or power law decay (the last case is known as scale-free behaviour Barabási and Albert 1999). In turn, collected empirical data has lead to the development of a number of simulated growth models for PTN. In Berche et al. (2009), interacting self-avoiding walks on a 2D lattice with preferential attachment rules are applied to produce similar statistics to real world PTN. In Torres et al. (2011), an optimisation model for line planning is discussed considering the competing interests in maintaining a quality service whilst minimising costs. In Yang et al. (2011), PTN are grown a route for each time step using an ideal n-depth clique topology. In Sui et al. (2012), the optimised growth of a route is considered by using two competing factors: investors and clients; clients want the route to be as straight as possible to save time whereas investors want the routes to meander in order to collect as many passengers to maximise profits. As it has been shown recently (Louf, Roth, and Barthelemy 2014), the cost–benefit analysis accounts for the scaling relations that govern dependency of the PTN characteristics with the socio-economical features of the underlying region.