| Id |
Subject |
Object |
Predicate |
Lexical cue |
| T409 |
0-118 |
Sentence |
denotes |
Diffusion is the random, translational motion of molecules in solution as a consequence of their thermal energy [285]. |
| T410 |
119-282 |
Sentence |
denotes |
This type of motion is often referred to as “Brownian motion”, a motion that describes molecular movement induced by random collisions between the molecules [286]. |
| T411 |
283-482 |
Sentence |
denotes |
In the presence of a concentration gradient, molecules will naturally move from places of higher concentration to places of lower concentration [287] after a period of time, t, as shown in Figure 11. |
| T412 |
483-543 |
Sentence |
denotes |
Fick’s Law can be used to model this type of movement [288]. |
| T413 |
544-743 |
Sentence |
denotes |
The distribution of the diffusing molecules is accurately represented by a Gaussian curve, a normal distribution centered at a single point, which gradually “flattens” as t approaches infinity [213]. |
| T414 |
744-839 |
Sentence |
denotes |
The extent to which a molecule diffuses is directly related to its shape, size, and mass [285]. |
| T415 |
840-1073 |
Sentence |
denotes |
In homogeneous isotropic solutions, the root mean square distance (zrms) traveled by a molecule is given by following equation [289,290]:zrms=(2Dt)12 where D is the diffusion coefficient of the molecule, and t is the diffusion time. |
| T416 |
1074-1428 |
Sentence |
denotes |
Making the assumption that the molecules are solid rigid spheres, the value of D can be calculated according to the famous Einstein-Stokes equation (Equation (2)):(4) D=kbT6πηrs where kb is the Boltzmann’s constant (1.3807 × 10−23 J/K), T is the absolute temperature, η is the solution viscosity, and rs is the hydrodynamic radius of the molecule [290]. |
| T417 |
1429-1671 |
Sentence |
denotes |
Equation (1) and Equation (2), however, are not universally applicable; they only apply to molecules that are freely diffusing in isotropic, homogeneous solutions, and importantly that can be accurately described as hard, rigid spheres [285]. |
| T418 |
1672-1884 |
Sentence |
denotes |
Different molecular geometries and additional modes of diffusion (i.e., restricted and anisotropic) require more advanced mathematics and theory [291,292], but the essential concepts of diffusion remain the same. |
