# Molecular Gels: Materials with Self-Assembled Fibrillar by Richard G Weiss, Pierre Terech

By Richard G Weiss, Pierre Terech

"Molecular Gels: fabrics with Self-Assembled Fibrillar Networks" is a finished treatise on gelators, specifically low molecular-mass gelators and the houses in their gels. The constructions and modes of formation of the self-assembled fibrillar networks (SAFINs) that immobilize the liquid elements of the gels are mentioned experimentally and theoretically. The spectroscopic, rheological, and structural positive aspects of different sessions of low molecular-mass gelators also are offered. Many examples of the applying of the important analytical recommendations for research of molecular gels (including SANS, SAXS, WAXS, UV-vis absorption, fluorescence and CD spectroscopies, scanning electron, transmission electron and optical microscopies, and molecular modeling) are provided didactically and in-depth, as are a number of of the theories of the levels of aggregation of person low molecular-mass gelator molecules resulting in SAFINs. numerous genuine and capability purposes of molecular gels in disparate fields (from silicate replication of nanostructures to paintings conservation) are defined. certain emphasis is put on views for destiny advancements. This e-book is a useful source for researchers and practitioners both already learning self-assembly and delicate topic or new to the realm. those that will locate the booklet invaluable comprise chemists, engineers, spectroscopists, physicists, biologists, theoreticians, and fabrics scientists.

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**Example text**

The cluster size l for which the volume fraction φl becomes largest is: ∂ l /∂l = 1 + ln x (93) Figure 10. (Top) The binding free energy per molecule as a function of the aggregation number. (Bottom) Total volume fraction as a function of the unimer concentration. Type I leads to micellization with a ﬁnite aggregation number. Type II and Type III lead to macroscopic aggregates, such as inﬁnitely long cylindrical micelles and three dimensional networks. In the latter case, the volume fraction φ1 of the molecules that remain unassociated in the solution as a function of the total volume fraction φ of the molecules shows a singularity at the point where the weight average molecular weight of aggregates becomes inﬁnite.

The binding free energy is expanded around l ∗ : 1∼ = a − b(l − l ∗ )2 + · · · l a and b are positive constants. Since the volume fraction of l-mers is: 1 − δl − φl = e−bl( l)2 (ea φ1 )l (96) (97) The cmc is determined from the condition: (φ1 )cmc = e−a (98) Hence, we have Eq. , the distribution √ function of micelles becomes Gaussian with mean value l ∗ and variance 1/ 2l ∗ b). 2. l)2 (99) Gelation by Pairwise Association Consider the simplest gelling binary mixture in which primary functional molecules form networks in a solvent [10–12].

110). x ≡ f λφ1 /n = f λν1 (110) 50 F. Tanaka It gives the number of functional groups f φ1 /n carried by the unassociated polymer chains in the solution, multiplied by the association constant λ(T ) as a temperature shift factor. From this distribution function, we can obtain average values of physical quantities. First, the total number concentration of the ﬁnite clusters is given by: νl = S0 (x) λ (111) l≥1 Their volume fraction is: λ φl = S1 (x) n l≥1 (112) Therefore, the number average of the cluster size is given by: l¯n ≡ νl = S1 (x)/S0 (x) lνl (113) The weight average is: l¯w ≡ l 2 νl lνl = S2 (x)/S1 (x) (114) These are written in terms of the moments of Stockmayer’s distribution function deﬁned by: Sk (x) ≡ ∞ l k ωl x l (k = 0, 1, 2, .