Strong attractive interaction between finite element models of twisted cellulose nanofibers by intermeshing of twists

Analysis of the attractive interaction between intrinsically twisted cellulose nanofibers (CNFs) is essential to control the physical properties of the higher-order structures of CNFs, such as paper and spun fiber. In this study, a finite element model reflecting the typical morphology of a twisted CNF was used to analyze the attractive interaction forces between multiple approaching CNF models. For two parallel CNF models, when one of the CNF models was rotated 90° around the long-axis direction, the twisting periods meshed, giving the maximum attraction force. Conversely, when the two CNF models were approaching diagonally, the CNF models were closest at an angle of −3.2° (i.e., in left-handed chirality) to give the most stable structure owing to the right-handed twist of the CNF models themselves. Furthermore, the two nematic layers were closest when one nematic layer was approached at an angle of −2° (i.e., in left-handed accumulation chirality), resulting in the greatest attraction. The results characterize the unique distribution of the attractive interaction forces between twisted CNF models, and they underscore the importance of chiral management in CNF aggregates, especially intermeshing of twists.

. ε values for the proximity combinations of each two planes of the twisted CNF model defined in Figure 1. Table S2. r0 values for the proximity combinations of each two plane of the twisted CNF model defined in Figure 1.   Figure S2. Relationship between Min. PE and Dy between the two parallel CNF models with 90° different Xrotate shown in Figure 5.

Appendix 1
The following structural design was applied to evaluate the approach distance, rotation angle, and PE of two groups of nematic layers with multiple twisted CNF models as one group. To maintain rotational symmetry around the z axis within the nematic layer, n CNF models were arranged in a circular shape with a diameter of 232 nm (corresponding to one twist cycle of a CNF model), parallel to the x axis and lineally symmetric with the x axis as the axis of symmetry. The coordinate settings for the CNF model comprising the first CNF layer are shown in Figure S3.
The y coordinate (ycenter) of the centerline in the x-axis direction was calculated by When n is odd, the CNF model is placed on the line with y = ycenter as the sweep axis.
When n is even, ycenter is between the CNF models. The y coordinate of CNF model 1 is set to 0, so ycenter ≠ r.
Next, the parameters required to design the nematic layer are the coordinates of the center of gravity of the CNF model end face, length of the CNF model in the x-axis direction, and angle of rotation around the x axis in each CNF model. Each parameter is generalized Figure S3. Coordinates of the nematic layer with multiple twisted CNF models. The straight lines represent the sweep axis (line of the center of gravity) of each model. and calculated so that the total number of CNF models n can be even or odd.
First, each parameter of the a-th CNF model is derived, as shown in Figure S4. For the coordinates of the center of gravity of the CNF model end faces Therefore, the distance between the centerline (y = ycenter) and ya is as follows: From this, the angle θa is The length of CNF model a is When CNF models are placed in parallel within the first CNF layer (the same relative arrangement as in Figure 4a with Xrotate = 0°), all of the CNF models must show the same cross-sectional shape in the same direction in a given yz plane. The angle of rotation for the part cut from each CNF model to be a circular array corresponds to xa. Thus, considering a set torsion period of 2π at 2r, the angle of rotation around the x axis that is subtracted from the CNF model per side (i.e., the angle of rotation subtracted by one length of the green double arrows in Figure S4) is Therefore, the angle of rotation around the x axis of CNF model a is When the layers were designed, as shown in Figure S5a, for example, with d = 10 nm and 23 CNF models, it was confirmed that the structure was correctly constructed as designed.
In particular, the cross sections of the CNF models in the same yz plane confirmed that all of the CNF models were oriented in the same direction. The second CNF layer was a duplicate of the first CNF layer, and it was placed by setting the parallel movement distances in x, y, and z directions and rotation angles around the x, y, and z axes of the entire group. When the second CNF layer was set to +50 nm in the z direction and Zrotate was set to −45°, we confirmed that the correct CNF model was constructed, as shown in Figure S5b.