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The number of configurations, c(n, m), of a single chain with length n attached to a flat surface with m monomers contacting the surface is exactly enumerated. A function of c(n, m) about m and n is obtained. From the function, a scaling law for mean energy of chain is derived, and we estimate the critical point ɛc = 0.276 and the crossover exponent ϕ = 0.5. The free energy difference between tethered...
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