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Instead of considering a real chain consisting of bonds and with fixed bond angles, torsion angles, and bond lengths, Kuhn considered an equivalent ideal chain with connected segments, now called Kuhn segments, that can orient in any random direction. The length of a fully stretched chain is = for the Kuhn segment chain. [5]
In other cases, a monomer is simply a segment of the polymer that can be modeled as behaving as a discrete, freely jointed unit. If so, l is the Kuhn length. For example, chromatin is modeled as a polymer in which each monomer is a segment approximately 14–46 kbp in length. [1]
The persistence length is considered to be one half of the Kuhn length, the length of hypothetical segments that the chain can be considered as freely joined. The persistence length equals the average projection of the end-to-end vector on the tangent to the chain contour at a chain end in the limit of infinite chain length. [4]
In physics, a characteristic length is an important dimension that defines the scale of a physical system. Often, such a length is used as an input to a formula in order to predict some characteristics of the system, and it is usually required by the construction of a dimensionless quantity, in the general framework of dimensional analysis and in particular applications such as fluid mechanics.
The distance from (x 0, y 0) to this line is measured along a vertical line segment of length |y 0 - (-c/b)| = |by 0 + c| / |b| in accordance with the formula. Similarly, for vertical lines (b = 0) the distance between the same point and the line is |ax 0 + c| / |a|, as measured along a horizontal line segment.
A persistence length of 51.35 nm and a contour length of 1560.9 nm were used for the model, which is depicted by the solid line. [4] Other biologically important polymers that can be effectively modeled as worm-like chains include: double-stranded DNA (persistence length 40-50 nm) and RNA (persistence length 64 nm) [3] [5]
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The Mark–Houwink equation, also known as the Mark–Houwink–Sakurada equation or the Kuhn–Mark–Houwink–Sakurada equation or the Landau–Kuhn–Mark–Houwink–Sakurada equation or the Mark-Chrystian equation gives a relation between intrinsic viscosity [] and molecular weight: [1] [2]