Block-copolymer model

Qu Y, Payne SC, Apkarian RP, ConticeUo VP. Self-assembly of a pol3rpeptide multi-block copolymer modeled on draghne silk proteins. J Am Chem Soc 2000 122 5014-5015. 

The adsorption of proteins at fluid interfaces is a key step in the stabilization of numerous food and non-food foams and emulsions.1 Our general goal is to relate the amino acid sequence of proteins to their surface properties, e. g. to the equation of state or other structural and thermodynamic properties. To improve this understanding, the effect of guanidine hydrochloride (Gu HC1) on /1-casein adsorption is evaluated in the framework of the block-copolymer model for the adsorption of this protein. At first the main features of the model are presented, and then the effect of Gu HC1 is interpreted using the previously introduced concepts. 

Fig. 48a. Normalized inverse scattering intensity NS l(q, e) observed in the Monte Carlo simulation of a block copolymer model on the simple cubic lattice (see Fig. 44) plotted vs the normalized inverse temperature eN. b Reciprocal structure factor S (q ) -l(cxrcfes, left scale) and q ( squares, right scale) plotted vs temperature for a nearly symmetric diblock copolymer of polystyrene/poly (cis— 1,4) isoprene (Mw = 15 700). Filled symbols refer to cooling, open symbols to heating runs. The straight tine indicates the extrapolation to a spinodal temperature (T,) that occurs above the actual transition temperature (Tmst). where the data show a jump. From Stuhn et al. [323],...

The effective chi-parameter is given by the k-dependent generalization d Eq. (6.17). If a small angle approximation where )CiNc(k) is constant is invdred, then Eq. (9.S) is identical in form with Leibler s RPA result [87] and the spinodal condition is far simpler than Eq. (9.4). However, since the true chi- Kiranieter is a wavevector-dependent correlation function, not a phenomenological number, it is functionally related to all the other intramolecular and intermolecular pair correlations in the system. This non-mean-field feature has many important consequences such as the fact that k" is influenced by many chain correlations [86,88]. It must be emphasized that although Eq. (9.5) should be accurate for the hypothetical symmetric block copolymer model, since it does not properly treat compressibility effects it is expected to be inadequate for most real copolymer systems. 

This fact has been explicitly demonstrated by simulating the block copolymer model of Fig. 7.16 in a I- x L x ) thin film geometry, where at the two repulsive walls of hnear dimensions I- x L an energy parameter 5 > 0 was appUed, which is repulsive to the A-monomers only. Choosing in the bulk aa = caa = ab > 0, and as = abI2., there is a tendency for the... 

Fig. 7.18 Profiles of the order parameter p z) - psiz) for the symmetric (/= 1/2) block copolymer model with N = 16,= 0.2, and Lx Lx D simple cubic lattices with periodic boundary conditions in the x and y directions, while at the two repulsive walls of size Lx L a repulsive energy of strength eAs = ab/2 acts on A-monomers, with units such that As/ka = 1- Linear dimension L in parallel directions is always L = 16, while the linear dimension in z-direction is D = 10 (a), 14 (b), and 18 (c). Normalized inverse temperatures are indicated by different symbols l/T = 0.3 (circles), 0.4 (diamonds), 0.5 (triangles), and 0.6 (squares). The critical temperature in the bulk is estimated as l/Tc 0.52 0.05. (From Kikuchi and Binder.

Fig. 7.40 Snapshot picture of typical configurations of the symmetrical block copolymer model (chain length N = 16,/ = 1/2, = 0.2) of Fig. 7.16 in a thin film geometry Lx Lx D, with...

The first case concerns particles with polymer chains attached to their surfaces. This can be done using chemically (end-)grafted chains, as is often done in the study of model colloids. Alternatively, a block copolymer can be used, of which one of the blocks (the anchor group) adsorbs strongly to the particles. The polymer chains may vary from short alkane chains to high molecular weight polymers (see also section C2.6.2). The interactions between such... 

The distinctive properties of densely tethered chains were first noted by Alexander [7] in 1977. His theoretical analysis concerned the end-adsorption of terminally functionalized polymers on a flat surface. Further elaboration by de Gennes [8] and by Cantor [9] stressed the utility of tethered chains to the description of self-assembled block copolymers. The next important step was taken by Daoud and Cotton [10] in 1982 in a model for star polymers. This model generalizes the... 

ADMET is quite possibly the most flexible transition-metal-catalyzed polymerization route known to date. With the introduction of new, functionality-tolerant robust catalysts, the primary limitation of this chemistry involves the synthesis and cost of the diene monomer that is used. ADMET gives the chemist a powerful tool for the synthesis of polymers not easily accessible via other means, and in this chapter, we designate the key elements of ADMET. We detail the synthetic techniques required to perform this reaction and discuss the wide range of properties observed from the variety of polymers that can be synthesized. For example, branched and functionalized polymers produced by this route provide excellent models (after quantitative hydrogenation) for the study of many large-volume commercial copolymers, and the synthesis of reactive carbosilane polymers provides a flexible route to solvent-resistant elastomers with variable properties. Telechelic oligomers can also be made which offer an excellent means for polymer modification or incorporation into block copolymers. All of these examples illustrate the versatility of ADMET. 

The purpose of this review is to show how anionic polymerization techniques have successfully contributed to the synthesis of a great variety of tailor-made polymer species Homopolymers of controlled molecular weight, co-functional polymers including macromonomers, cyclic macromolecules, star-shaped polymers and model networks, block copolymers and graft copolymers. 

The stable C-halogen bond formed can be used, however, for the formation of block copolymers by reinitiation with stronger Lewis acids. The electronic conditions in the model complex... 

The above equations gave reasonably reliable M value of SBS. Another approach to modeling the elastic behavior of SBS triblock copolymer has been developed [202]. The first one, the simple model, is obtained by a modification of classical rubber elasticity theory to account for the filler effect of the domain. The major objection was the simple application of mbber elasticity theory to block copolymers without considering the effect of the domain on the distribution function of the mbber matrix chain. In the derivation of classical equation of rabber elasticity, it is assumed that the chain has Gaussian distribution function. The use of this distribution function considers that aU spaces are accessible to a given chain. However, that is not the case of TPEs because the domain also takes up space in block copolymers. 

An important polymer modification reaction is the grafting to or from a polymer backbone by some chemical method to produce a branched structure Q). The characterization of the products of these reactions is often somewhat less well defined than block copolymers (2) due to the complexity of the mixture of products formed. It is therefore useful to prepare and characterize more well defined branched systems as models for the less well defined copolymers. The macromonomer method (3 ) allows for the preparation of more well defined copolymers than previously available. 

Various types of power law relaxation have been observed experimentally or predicted from models of molecular motion. Each of them is defined in its specific time window and for specific molecular structure and composition. Examples are dynamically induced glass transition [90,161], phase separated block copolymers [162,163], polymer melts with highly entangled linear molecules of uniform length [61,62], and many others. A comprehensive review on power law relaxation has been recently given by Winter [164],... 

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