Cross-linked polymer chains: Scaling and exact results

2008 ◽  
pp. 403-413
Author(s):  
Thomas A. Vilgis ◽  
Michael P. Solf
Keyword(s):  
Polymer Chains ◽  
Exact Results

Shape of Confined Polymer Chains

1997 ◽  
Vol 7 (3) ◽  
pp. 433-447 ◽  
Author(s):  
C. E. Cordeiro ◽  
M. Molisana ◽  
D. Thirumalai
Keyword(s):  
Polymer Chains ◽  
Confined Polymer ◽  
Confined Polymer Chains

Erratum - Frustration in periodic systems : exact results for some 2D ising models

1979 ◽  
Vol 40 (10) ◽  
pp. 1024-1024
Author(s):  
G. André ◽  
R. Bidaux ◽  
J.-P. Carton ◽  
R. Conte ◽  
L. de Seze
Keyword(s):  
Ising Models ◽  
Periodic Systems ◽  
Exact Results

Dynamics of polymer chains trapped in a slit

1977 ◽  
Vol 38 (10) ◽  
pp. 1285-1291 ◽  
Author(s):  
F. Brochard
Keyword(s):  
Polymer Chains

Almost empty polygons

2003 ◽  
Vol 40 (3) ◽  
pp. 269-286 ◽  
Author(s):  
H. Nyklová
Keyword(s):  
Exact Results ◽  
Point Sets ◽  
Planar Point ◽  
Convex Position ◽  
Vertex Set ◽  
Point Set ◽  
Empty Polygons

In this paper we study a problem related to the classical Erdos--Szekeres Theorem on finding points in convex position in planar point sets. We study for which n and k there exists a number h(n,k) such that in every planar point set X of size h(n,k) or larger, no three points on a line, we can find n points forming a vertex set of a convex n-gon with at most k points of X in its interior. Recall that h(n,0) does not exist for n = 7 by a result of Horton. In this paper we prove the following results. First, using Horton's construction with no empty 7-gon we obtain that h(n,k) does not exist for k = 2(n+6)/4-n-3. Then we give some exact results for convex hexagons: every point set containing a convex hexagon contains a convex hexagon with at most seven points inside it, and any such set of at least 19 points contains a convex hexagon with at most five points inside it.

SuFExable Polymers with Helical Structures Derived from Thionyl Tetrafluoride (SOF4)

2019 ◽  
Author(s):  
Suhua Li ◽  
Gencheng Li ◽  
Bing Gao ◽  
Sidharam P. Pujari ◽  
Xiaoyan Chen ◽  
...  
Keyword(s):  
Functional Polymers ◽  
Polymer Chains ◽  
New Materials ◽  
Helical Structures ◽  
Polymer Backbone ◽  
Silyl Ethers ◽  
Helical Polymer ◽  
Key Characteristics ◽  
Post Modification ◽  
Individual Polymer

The first SuFEx click chemistry synthesis of SOF<sub>4</sub>-derived copolymers based upon the polymerization of bis(iminosulfur oxydifluorides) and bis(aryl silyl ethers) is described. This novel class of SuFEx polymer presents two key characteristics: First, the newly created [-N=S(=O)F-O-] polymer backbone linkages are themselves SuFExable and primed to undergo further high-yielding and precise SuFEx-based post-modification with phenols or amines to yield branched functional polymers. Second, studies of individual polymer chains of several of these new materials indicate the presence of helical polymer structures, which itself suggests a preferential approach of new monomers onto the growing polymer chain upon the formation of the stereogenic linking moiety.

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