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FIG. 8. Center of mass distribution f(z) for all L = 16. z:coordinate of the center of mass, — — :model calculation, —— :SAW with N = 150; error in- creases from less than 0.0004 for |z|>5 to 0.02 for |z| = 0.

Figure 8 Center of mass distribution f(z) for all L = 16. z:coordinate of the center of mass, — — :model calculation, —— :SAW with N = 150; error in- creases from less than 0.0004 for |z|>5 to 0.02 for |z| = 0.

Related Figures (6)

FIG. 1. (S?)/(S?), as a function of A. A:N = 39, A:N = 79, D:N = 159, @:N = 319, O:N = 639; maximum error is 0.12 for all N. Figures 2-4 show (A;)/(A;)o as a function of A. The largest principal component remains nearly constant for A> 1.5, then decreases slightly and finally increases again for Ac], until it reaches the limiting two-dimensional value. This behavior is not unlike that of the mean-square radius of gyration discussed before. The second largest principal com- ponent behaves similarly, although the deviation from the plateau value occurs at a slightly smaller value of A. The smallest principal component, finally, remains constant for A>1. For smaller distances between the plates, it gradually decreases towards the limiting value of zero. Before we dis-
FIG. 1. (S?)/(S?), as a function of A. A:N = 39, A:N = 79, D:N = 159, @:N = 319, O:N = 639; maximum error is 0.12 for all N. Figures 2-4 show (A;)/(A;)o as a function of A. The largest principal component remains nearly constant for A> 1.5, then decreases slightly and finally increases again for Ac], until it reaches the limiting two-dimensional value. This behavior is not unlike that of the mean-square radius of gyration discussed before. The second largest principal com- ponent behaves similarly, although the deviation from the plateau value occurs at a slightly smaller value of A. The smallest principal component, finally, remains constant for A>1. For smaller distances between the plates, it gradually decreases towards the limiting value of zero. Before we dis-
FIG. 3. (A,)/(A,) as a function of A. A:N = 39, A:N = 79, O:N = 159, @:N = 319, O:N = 639; maximum error increases from 0.07 for NV = 39 to 0.14 for N = 639.
FIG. 3. (A,)/(A,) as a function of A. A:N = 39, A:N = 79, O:N = 159, @:N = 319, O:N = 639; maximum error increases from 0.07 for NV = 39 to 0.14 for N = 639.
FIG. 4. (A,)/(A;), as a function of A. A:N = 39, A:N = 79, O:N = 159, @:N = 319, O:N = 639; maximum error is 0.06 for all N. The results presented so far provide ample evidence for the statement that the primary effect of confinement on flexi- ble polymers in a dilute good solvent is to align rather than to deform the coil. Now, these results will be compared with the exact results of an analytic model. In the foregoing, the mean-square principal radii of gyration were used to charac- terize the average shape of the polymer coil. But more appro- priate lengths, as far as the interaction between the plates and the coil is concerned, are the so-called spans. The span or extent of a self-avoiding walk in a given direction is defined initially, the decrease in value of the orientation function
FIG. 4. (A,)/(A;), as a function of A. A:N = 39, A:N = 79, O:N = 159, @:N = 319, O:N = 639; maximum error is 0.06 for all N. The results presented so far provide ample evidence for the statement that the primary effect of confinement on flexi- ble polymers in a dilute good solvent is to align rather than to deform the coil. Now, these results will be compared with the exact results of an analytic model. In the foregoing, the mean-square principal radii of gyration were used to charac- terize the average shape of the polymer coil. But more appro- priate lengths, as far as the interaction between the plates and the coil is concerned, are the so-called spans. The span or extent of a self-avoiding walk in a given direction is defined initially, the decrease in value of the orientation function
IG. 6. (cos? #8) as a function of A. &A:N = 39, A:N=79, O:N = 159 ):N = 319, O:N = 639, —-—:model calculation, ——- :SAW; maximur rror in (cos? 8 ) is 0.05 for all N.
IG. 6. (cos? #8) as a function of A. &A:N = 39, A:N=79, O:N = 159 ):N = 319, O:N = 639, —-—:model calculation, ——- :SAW; maximur rror in (cos? 8 ) is 0.05 for all N.
FIG. 5. (cos? a) as a function of A. A:N = 39, A:N = 79, O:N = 159, @:N = 319, O:N = 639, ~-:model calculation, ——:SAW; maximum error in (cos” a) increases from 0.03 for NV = 39 to 0.05 for NV = 639.
FIG. 5. (cos? a) as a function of A. A:N = 39, A:N = 79, O:N = 159, @:N = 319, O:N = 639, ~-:model calculation, ——:SAW; maximum error in (cos” a) increases from 0.03 for NV = 39 to 0.05 for NV = 639.
FIG. 7. (cos? y) as a function of A.A:N = 39, AW = 79, O:N = 159, @:N = 319, O:N = 639, —- :model calculation, ——:SAW; maximum error in (cos? 7) is 0.065 for all N.
FIG. 7. (cos? y) as a function of A.A:N = 39, AW = 79, O:N = 159, @:N = 319, O:N = 639, —- :model calculation, ——:SAW; maximum error in (cos? 7) is 0.065 for all N.
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