- Source: Layer by Layer
- Source: Layer by layer
The layer" target="_blank">Layer by layer" target="_blank">Layer method, also known as the beginners' method, is a method of solving the 3x3x3 Rubik's Cube. Many beginners' methods use this approach, and it also forms the basis of the CFOP speedcubing technique.
History
The layer" target="_blank">Layer by layer" target="_blank">Layer Method was pioneered by David Singmaster in his 1980 book Notes on Rubik's "Magic Cube". The same idea was adopted by James G. Nourse in his The Simple Solution to Rubik's Cube which became the bestselling book of 1981, and similar approaches could be found in Don Taylor's Mastering Rubik's Cube and Cyril Östrop's Solving the Cube from the same era.
Method
The method begins with the puzzle solver making a cross on one face with the edge pieces ensuring that all edge colours match the adjacent center colours (step 1 in the diagram below), then putting the corners into position between the edges (step 2). The first layer" target="_blank">layer is then complete. In step 3, the four edge pieces of the middle layer" target="_blank">layer are solved. At this point the first two layers are solved. In step 4, a cross of the opposite color is made on the last layer" target="_blank">layer. For step 5, the last layer" target="_blank">layer edges are permuted (swapped around). In step 6, the last layer" target="_blank">layer corners are permuted. Finally, the last layer" target="_blank">layer corners are oriented.
Most layer" target="_blank">Layer by layer" target="_blank">Layer beginners' methods solve the first two layers using the same technique. However, there are many variant techniques for the final layer" target="_blank">layer, depending on whether the corner or edge pieces are solved first. For example:
Top layer" target="_blank">layer "white cross": F' U L' U' or F R U R' U' F'
Top layer" target="_blank">layer left corner: D L D' L’ / right corner: D' R' D R
Second layer" target="_blank">layer right edge: U R U' R' U' F' U F / Left edge: U' L' U L U F U' F'
Final layer" target="_blank">layer cross (edge orientation): F R U R' U' F'
Final layer" target="_blank">layer edge permutation: R U R' U R U U R'
Final layer" target="_blank">layer corner orientation: U R U' L' U R' U' L
Final layer" target="_blank">layer corner permutation: R' D' R D
CFOP method
The CFOP speedcubing technique, developed by Jessica Fridrich and others in the 1980s, similarly divides the puzzle into layers to be solved. However, the method uses far more algorithms than the beginners' methods, making it harder to learn, but faster to execute once mastered.
References
layer" target="_blank">Layer-by-layer" target="_blank">layer (LbL) deposition is a thin film fabrication technique. The films are formed by depositing alternating layers of oppositely charged materials with wash steps in between. This can be accomplished by using various techniques such as immersion, spin, spray, electromagnetism, or fluidics.
Development
The first implementation of this technique is attributed to J. J. Kirkland and R. K. Iler of DuPont, who carried it out using microparticles in 1966. The method was later revitalized by the discovery of its applicability to a wide range of polyelectrolytes by Gero Decher at Johannes Gutenberg-Universität Mainz.
Implementation
A simple representation can be made by defining two oppositely charged polyions as + and -, and defining the wash step as W. To make an LbL film with 5 bilayers one would deposit W+W-W+W-W+W-W+W-W+W-W, which would lead to a film with 5 bilayers, specifically + - + - + - + - + - .
The representation of the LbL technique as a multilayer build-up based solely on electrostatic attraction is a simplification. Other interactions are involved in this process, including hydrophobic attraction. Multilayer build-up is enabled by multiple attractive forces acting cooperatively, typical for high-molecular weight building blocks, while electrostatic repulsion provides self-limitation of the absorption of individual layers. This range of interactions makes it possible to extend the LbL technique to hydrogen-bonded films, nanoparticles, similarly charged polymers, hydrophobic solvents, and other unusual systems.
The bilayers and wash steps can be performed in many different ways including dip coating, spin-coating, spray-coating, flow based techniques and electro-magnetic techniques. The preparation method distinctly impacts the properties of the resultant films, allowing various applications to be realized. For example, a whole car has been coated with spray assembly, optically transparent films have been prepared with spin assembly, etc. Characterization of LbL film deposition is typically done by optical techniques such as dual polarisation interferometry or ellipsometry or mechanical techniques such as quartz crystal microbalance.
LbL offers several advantages over other thin film deposition methods. LbL is simple and can be inexpensive. There are a wide variety of materials that can be deposited by LbL including polyions, metals, ceramics, nanoparticles, and biological molecules. Another important quality of LbL is the high degree of control over thickness, which arises due to the variable growth profile of the films, which directly correlates to the materials used, the number of bilayers, and the assembly technique. By the fact that each bilayer can be as thin as 1 nm, this method offers easy control over the thickness with 1 nm resolution.
Applications
LbL has found applications in protein purification, corrosion control, (photo)electrocatalysis, biomedical applications, ultrastrong materials, and many more. LbL composites from graphene oxide harbingered the appearance of numerous graphene and graphene oxide composites later on. The first use of reduced graphene oxide composites for lithium batteries was also demonstrated with LbL multilayers.
See also
Atomic layer" target="_blank">layer deposition
References
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