\(\renewcommand{\AA}{\text{Å}}\)

# fix wall/lj93 command

Accelerator Variants: wall/lj93/kk

# fix wall/lj126 command

# fix wall/lj1043 command

# fix wall/colloid command

# fix wall/harmonic command

# fix wall/harmonic/outside command

# fix wall/lepton command

# fix wall/morse command

# fix wall/table command

## Syntax

    fix ID group-ID style [tabstyle] [N] face args ... keyword value ...

- ID, group-ID are documented in fix command

- style = wall/lj93 or wall/lj126 or wall/lj1043 or wall/colloid or wall/harmonic or wall/harmonic/outside or wall/lepton or wall/morse or wall/table

- tabstyle = linear or spline = method of table interpolation (only applies to wall/table)

- N = use N values in linear or spline interpolation (only applies to wall/table)

- one or more face/arg pairs may be appended

- face = xlo or xhi or ylo or yhi or zlo or zhi

- args for styles lj93 or lj126 or lj1043 or colloid or harmonic

      args = coord epsilon sigma cutoff
      coord = position of wall = EDGE or constant or variable
        EDGE = current lo or hi edge of simulation box
        constant = number like 0.0 or -30.0 (distance units)
        variable = equal-style variable like v_x or v_wiggle
      epsilon = strength factor for wall-particle interaction (energy or energy/distance^2 units)
        epsilon can be a variable (see below)
      sigma = size factor for wall-particle interaction (distance units)
        sigma can be a variable (see below)
      cutoff = distance from wall at which wall-particle interactions are cut off (distance units)

- args for style lepton

      args = coord expression cutoff
      coord = position of wall = EDGE or constant or variable
        EDGE = current lo or hi edge of simulation box
        constant = number like 0.0 or -30.0 (distance units)
        variable = equal-style variable like v_x or v_wiggle
      expression = Lepton expression for the potential  (energy units)
      cutoff = distance from wall at which wall-particle interactions are cut off (distance units)

- args for style morse

      args = coord D_0 alpha r_0 cutoff
      coord = position of wall = EDGE or constant or variable
        EDGE = current lo or hi edge of simulation box
        constant = number like 0.0 or -30.0 (distance units)
        variable = equal-style variable like v_x or v_wiggle
      D_0 = depth of the potential (energy units)
        D_0 can be a variable (see below)
      alpha = width factor for wall-particle interaction (1/distance units)
        alpha can be a variable (see below)
      r_0 = distance of the potential minimum from the face of region (distance units)
        r_0 can be a variable (see below)
      cutoff = distance from wall at which wall-particle interactions are cut off (distance units)

- args for style table

      args = coord filename keyword cutoff
      coord = position of wall = EDGE or constant or variable
        EDGE = current lo or hi edge of simulation box
        constant = number like 0.0 or -30.0 (distance units)
        variable = equal-style variable like v_x or v_wiggle
      filename = file containing tabulated energy and force values
      keyword = section identifier to select a specific table in table file
      cutoff = distance from wall at which wall-particle interactions are cut off (distance units)

- zero or more keyword/value pairs may be appended

- keyword = units or fld or pbc

      units value = lattice or box
        lattice = the wall position is defined in lattice units
        box = the wall position is defined in simulation box units
      fld value = yes or no
        yes = invoke the wall constraint to be compatible with implicit FLD
        no = invoke the wall constraint in the normal way
      pbc value = yes or no
        yes = allow periodic boundary in a wall dimension
        no = require non-perioidic boundaries in any wall dimension

## Examples

    fix wallhi all wall/lj93 xlo -1.0 1.0 1.0 2.5 units box
    fix wallhi all wall/lj93 xhi EDGE 1.0 1.0 2.5
    fix wallhi all wall/harmonic xhi EDGE 100.0 0.0 4.0 units box
    fix wallhi all wall/morse xhi EDGE 1.0 1.0 1.0 2.5 units box
    fix wallhi all wall/lj126 v_wiggle 23.2 1.0 1.0 2.5
    fix zwalls all wall/colloid zlo 0.0 1.0 1.0 0.858 zhi 40.0 1.0 1.0 0.858
    fix xwall mobile wall/table spline 200 EDGE -5.0 walltab.dat HARMONIC 4.0
    fix xwalls mobile wall/lepton xlo -5.0 "k*(r-rc)^2;k=100.0" 4.0 xhi 5.0 "k*(r-rc)^2;k=100.0" 4.0

## Description

Bound the simulation domain on one or more of its faces with a flat wall that interacts with the atoms in the group by generating a force on the atom in a direction perpendicular to the wall. The energy of wall-particle interactions depends on the style.

For style wall/lj93, the energy E is given by the 9-3 Lennard-Jones potential:

\[E = \epsilon \left[ \frac{2}{15} \left(\frac{\sigma}{r}\right)^{9} - \left(\frac{\sigma}{r}\right)^3 \right] \qquad r < r_c\]

For style wall/lj126, the energy E is given by the 12-6 Lennard-Jones potential:

\[E = 4 \epsilon \left[ \left(\frac{\sigma}{r}\right)^{12} - \left(\frac{\sigma}{r}\right)^6 \right] \qquad r < r_c\]

For style wall/lj1043, the energy E is given by the 10-4-3 Lennard-Jones potential:

\[E = 2 \pi \epsilon \left[ \frac{2}{5} \left(\frac{\sigma}{r}\right)^{10} - \left(\frac{\sigma}{r}\right)^4 - \frac{\sqrt(2)\sigma^3}{3\left(r+\left(0.61/\sqrt(2)\right)\sigma\right)^3}\right] \qquad r < r_c\]

For style wall/colloid, the energy E is given by an integrated form of the pair_style colloid potential:

\[\begin{split}E = & \epsilon \left[ \frac{\sigma^{6}}{7560} \left(\frac{6R-D}{D^{7}} + \frac{D+8R}{(D+2R)^{7}} \right) \right. \\ & \left. - \frac{1}{6} \left(\frac{2R(D+R) + D(D+2R) \left[ \ln D - \ln (D+2R) \right]}{D(D+2R)} \right) \right] \qquad r < r_c\end{split}\]

For style wall/harmonic, the energy E is given by a repulsive-only harmonic spring potential:

\[E = \epsilon \quad (r - r_c)^2 \qquad r < r_c\]

For style wall/harmonic/outside, the energy E is given by an attractive-only harmonic spring potential for selected atoms group passing outside the wall placed at \(w_0\) up to a cutoff distance \(r_c\): .. math:

    E = \epsilon \quad (r - w_0)^2 \qquad r < r_c

For style wall/morse, the energy E is given by a Morse potential:

\[E = D_0 \left[ e^{- 2 \alpha (r - r_0)} - 2 e^{- \alpha (r - r_0)} \right] \qquad r < r_c\]

For style wall/harmonic/outside, the formulation avoids the presence of repulsive bands inside a controlled volume preventing the definition of a precise volumetric concentration (see example scripts for 2D visualization). Instead, the particles are allowed to go outside by a small amount, getting a finer definition of the concentration inside the controlled volume, as employed for the CMC determination in Barraud et al (Barraud).

Added in version 28Mar2023.

For style wall/lepton, the energy E is provided as an Lepton expression string using “r” as the distance variable. The Lepton library, that the wall/lepton style interfaces with, evaluates this expression string at run time to compute the wall-particle energy. It also creates an analytical representation of the first derivative of this expression with respect to “r” and then uses that to compute the force between the wall and atoms in the fix group. The Lepton expression must be either enclosed in quotes or must not contain any whitespace so that LAMMPS recognizes it as a single keyword.

Optionally, the expression may use “rc” to refer to the cutoff distance for the given wall. Further constants in the expression can be defined in the same string as additional expressions separated by semicolons. The expression “k*(r-rc)^2;k=100.0” represents a repulsive-only harmonic spring as in fix wall/harmonic or wall/harmonic/outside with a force constant K (same as \(\epsilon\) above) of 100 energy units. More details on the Lepton expression strings are given below.

Added in version 28Mar2023.

For style wall/table, the energy E and forces are determined from interpolation tables listed in one or more files as a function of distance. The interpolation tables are used to evaluate energy and forces between particles and the wall similar to how analytic formulas are used for the other wall styles.

The interpolation tables are created as a pre-computation by fitting cubic splines to the file values and interpolating energy and force values at each of N distances. During a simulation, the tables are used to interpolate energy and force values as needed for each wall and particle separated by a distance R. The interpolation is done in one of two styles: linear or spline.

For the linear style, the distance R is used to find the 2 surrounding table values from which an energy or force is computed by linear interpolation.

For the spline style, cubic spline coefficients are computed and stored for each of the N values in the table, one set of splines for energy, another for force. Note that these splines are different than the ones used to pre-compute the N values. Those splines were fit to the Nfile values in the tabulated file, where often Nfile < N. The distance R is used to find the appropriate set of spline coefficients which are used to evaluate a cubic polynomial which computes the energy or force.

For each wall a filename and a keyword must be provided as in the examples above. The filename specifies a file containing tabulated energy and force values. The keyword specifies a section of the file. The format of this file is described below.

In all cases, r is the distance from the particle to the wall at position coord, and \(r_c\) is the cutoff distance at which the particle and wall no longer interact. The energy of the wall potential is shifted so that the wall-particle interaction energy is 0.0 at the cutoff distance.

Up to 6 walls or faces can be specified in a single command: xlo, xhi, ylo, yhi, zlo, zhi. A lo face interacts with particles near the lower side of the simulation box in that dimension. A hi face interacts with particles near the upper side of the simulation box in that dimension.

The position of each wall can be specified in one of 3 ways: as the EDGE of the simulation box, as a constant value, or as a variable. If EDGE is used, then the corresponding boundary of the current simulation box is used. If a numeric constant is specified then the wall is placed at that position in the appropriate dimension (x, y, or z). In both the EDGE and constant cases, the wall will never move. If the wall position is a variable, it should be specified as v_name, where name is an equal-style variable name. In this case the variable is evaluated each timestep and the result becomes the current position of the reflecting wall. Equal-style variables can specify formulas with various mathematical functions, and include thermo_style command keywords for the simulation box parameters and timestep and elapsed time. Thus it is easy to specify a time-dependent wall position. See examples below.

For the wall/lj93 and wall/lj126 and wall/lj1043 styles, \(\epsilon\) and \(\sigma\) are the usual Lennard-Jones parameters, which determine the strength and size of the particle as it interacts with the wall. Epsilon has energy units. Note that this \(\epsilon\) and \(\sigma\) may be different than any \(\epsilon\) or \(\sigma\) values defined for a pair style that computes particle-particle interactions.

The wall/lj93 interaction is derived by integrating over a 3d half-lattice of Lennard-Jones 12/6 particles. The wall/lj126 interaction is effectively a harder, more repulsive wall interaction. The wall/lj1043 interaction is yet a different form of wall interaction, described in Magda et al in (Magda).

For the wall/colloid style, R is the radius of the colloid particle, D is the distance from the surface of the colloid particle to the wall (r-R), and \(\sigma\) is the size of a constituent LJ particle inside the colloid particle and wall. Note that the cutoff distance Rc in this case is the distance from the colloid particle center to the wall. The prefactor \(\epsilon\) can be thought of as an effective Hamaker constant with energy units for the strength of the colloid-wall interaction. More specifically, the \(\epsilon\) prefactor is \(4\pi^2 \rho_{wall} \rho_{colloid} \epsilon \sigma^6\), where \(\epsilon\) and \(\sigma\) are the LJ parameters for the constituent LJ particles. \(\rho_{wall}\) and \(\rho_{colloid}\) are the number density of the constituent particles, in the wall and colloid respectively, in units of 1/volume.

The wall/colloid interaction is derived by integrating over constituent LJ particles of size \(\sigma\) within the colloid particle and a 3d half-lattice of Lennard-Jones 12/6 particles of size \(\sigma\) in the wall. As mentioned in the preceding paragraph, the density of particles in the wall and colloid can be different, as specified by the \(\epsilon\) prefactor.

For the wall/harmonic and wall/harmonic/outside style, \(\epsilon\) is effectively the spring constant K, and has units (energy/distance^2). The input parameter \(\sigma\) is ignored. The minimum energy position of the harmonic spring is at the cutoff. This is a repulsive-only spring since the interaction is truncated at the cutoff

For the wall/morse style, the three parameters are in this order: \(D_0\) the depth of the potential, \(\alpha\) the width parameter, and \(r_0\) the location of the minimum. \(D_0\) has energy units, \(\alpha\) inverse distance units, and \(r_0\) distance units.

For any wall that supports them, the \(\epsilon\) and/or \(\sigma\) and/or \(\alpha\) parameter can be specified as an equal-style variable, in which case it should be specified as v_name, where name is the variable name. As with a variable wall position, the variable is evaluated each timestep and the result becomes the current epsilon or sigma of the wall. Equal-style variables can specify formulas with various mathematical functions, and include thermo_style command keywords for the simulation box parameters and timestep and elapsed time. Thus it is easy to specify a time-dependent wall interaction.

Note

For all of the styles (except wall/harmonic/outside), you must ensure that r is always > 0 for all particles in the group, or LAMMPS will generate an error. This means you cannot start your simulation with particles at the wall position coord (r = 0) or with particles on the wrong side of the wall (r < 0). For the wall/lj93 and wall/lj126 styles, the energy of the wall/particle interaction (and hence the force on the particle) blows up as r -> 0. The wall/colloid style is even more restrictive, since the energy blows up as D = r-R -> 0. This means the finite-size particles of radius R must be a distance larger than R from the wall position coord. The harmonic style is a softer potential and does not blow up as r -> 0, but you must use a large enough \(\epsilon\) that particles always reamin on the correct side of the wall (r > 0).

The units keyword determines the meaning of the distance units used to define a wall position, but only when a numeric constant or variable is used. It is not relevant when EDGE is used to specify a face position. In the variable case, the variable is assumed to produce a value compatible with the units setting you specify.

A box value selects standard distance units as defined by the units command, e.g. Angstroms for units = real or metal. A lattice value means the distance units are in lattice spacings. The lattice command must have been previously used to define the lattice spacings.

The fld keyword can be used with a yes setting to invoke the wall constraint before pairwise interactions are computed. This allows an implicit FLD model using pair_style lubricateU to include the wall force in its calculations. If the setting is no, wall forces are imposed after pairwise interactions, in the usual manner.

The pbc keyword can be used with a yes setting to allow walls to be specified in a periodic dimension. See the boundary command for options on simulation box boundaries. The default for pbc is no, which means the system must be non-periodic when using a wall. But you may wish to use a periodic box. E.g. to allow some particles to interact with the wall via the fix group-ID, and others to pass through it and wrap around a periodic box. In this case you should ensure that the wall is sufficiently far enough away from the box boundary. If you do not, then particles may interact with both the wall and with periodic images on the other side of the box, which is probably not what you want.

Here are examples of variable definitions that move the wall position in a time-dependent fashion using equal-style variables. The wall interaction parameters (epsilon, sigma) could be varied with additional variable definitions.

    variable ramp equal ramp(0,10)
    fix 1 all wall xlo v_ramp 1.0 1.0 2.5

    variable linear equal vdisplace(0,20)
    fix 1 all wall xlo v_linear 1.0 1.0 2.5

    variable wiggle equal swiggle(0.0,5.0,3.0)
    fix 1 all wall xlo v_wiggle 1.0 1.0 2.5

    variable wiggle equal cwiggle(0.0,5.0,3.0)
    fix 1 all wall xlo v_wiggle 1.0 1.0 2.5

The ramp(lo,hi) function adjusts the wall position linearly from lo to hi over the course of a run. The vdisplace(c0,velocity) function does something similar using the equation position = c0 + velocity*delta, where delta is the elapsed time.

The swiggle(c0,A,period) function causes the wall position to oscillate sinusoidally according to this equation, where omega = 2 PI / period:

    position = c0 + A sin(omega*delta)

The cwiggle(c0,A,period) function causes the wall position to oscillate sinusoidally according to this equation, which will have an initial wall velocity of 0.0, and thus may impose a gentler perturbation on the particles:

    position = c0 + A (1 - cos(omega*delta))

## Lepton expression syntax and features

Lepton supports the following operators in expressions:

+ | Add |  | - | Subtract |  | * | Multiply |  | / | Divide |  | ^ | Power

The following mathematical functions are available:

sqrt(x) | Square root | exp(x) | Exponential
log(x) | Natural logarithm | sin(x) | Sine (angle in radians)
cos(x) | Cosine (angle in radians) | sec(x) | Secant (angle in radians)
csc(x) | Cosecant (angle in radians) | tan(x) | Tangent (angle in radians)
cot(x) | Cotangent (angle in radians) | asin(x) | Inverse sine (in radians)
acos(x) | Inverse cosine (in radians) | atan(x) | Inverse tangent (in radians)
sinh(x) | Hyperbolic sine | cosh(x) | Hyperbolic cosine
tanh(x) | Hyperbolic tangent | erf(x) | Error function
erfc(x) | Complementary Error function | abs(x) | Absolute value
min(x,y) | Minimum of two values | max(x,y) | Maximum of two values
delta(x) | delta(x) is 1 for x = 0, otherwise 0 | step(x) | step(x) is 0 for x < 0, otherwise 1

Numbers may be given in either decimal or exponential form. All of the following are valid numbers: 5, -3.1, 1e6, and 3.12e-2.

As an extension to the standard Lepton syntax, it is also possible to use LAMMPS variables in the format “v_name”. Before evaluating the expression, “v_name” will be replaced with the value of the variable “name”. This is compatible with all kinds of scalar variables, but not with vectors, arrays, local, or per-atom variables. If necessary, a custom scalar variable needs to be defined that can access the desired (single) item from a non-scalar variable. As an example, the following lines will instruct LAMMPS to ramp the force constant for a harmonic bond from 100.0 to 200.0 during the next run:

    variable fconst equal ramp(100.0, 200)
    bond_style lepton
    bond_coeff 1 1.5 "v_fconst * (r^2)"

An expression may be followed by definitions for intermediate values that appear in the expression. A semicolon “;” is used as a delimiter between value definitions. For example, the expression:

    a^2+a*b+b^2; a=a1+a2; b=b1+b2

is exactly equivalent to

    (a1+a2)^2+(a1+a2)*(b1+b2)+(b1+b2)^2

The definition of an intermediate value may itself involve other intermediate values. Whitespace and quotation characters (’'’ and ‘”’) are ignored. All uses of a value must appear before that value’s definition. For efficiency reasons, the expression string is parsed, optimized, and then stored in an internal, pre-parsed representation for evaluation.

Evaluating a Lepton expression is typically between 2.5 and 5 times slower than the corresponding compiled and optimized C++ code. If additional speed or GPU acceleration (via GPU or KOKKOS) is required, the interaction can be represented as a table. Suitable table files can be created either internally using the pair_write or bond_write command or through the Python scripts in the tools/tabulate folder.

## Table file format

Suitable tables for use with fix wall/table can be created by the Python code in the `tools/tabulate` folder of the LAMMPS source code distribution.

The format of a tabulated file is as follows (without the parenthesized comments):

    # Tabulated wall potential UNITS: real

    HARMONIC                       (keyword is the first text on a line)
    N 100 FP 200 200
                                   (blank line)
    1  0.04    1568.16    792.00   (index, distance to wall, energy, force)
    2  0.08    1536.64    784.00
    3  0.12    1505.44    776.00
    ...
    99  3.96      0.16      8.00
    100  4.00     0         0

A section begins with a non-blank line whose first character is not a “#”; blank lines or lines starting with “#” can be used as comments between sections. The first line begins with a keyword which identifies the section. The line can contain additional text, but the initial text must match the argument specified in the fix wall/table command. The next line lists (in any order) one or more parameters for the table. Each parameter is a keyword followed by one or more numeric values.

The parameter “N” is required and its value is the number of table entries that follow. Note that this may be different than the N specified in the fix wall/table command. Let Ntable = N in the fix command, and Nfile = “N” in the tabulated file. What LAMMPS does is a preliminary interpolation by creating splines using the Nfile tabulated values as nodal points. It uses these to interpolate as needed to generate energy and force values at Ntable different points. The resulting tables of length Ntable are then used as described above, when computing energy and force for wall-particle interactions. This means that if you want the interpolation tables of length Ntable to match exactly what is in the tabulated file (with effectively no preliminary interpolation), you should set Ntable = Nfile.

## Dump image info

Added in version 11Feb2026.

These wall fixes support the fix keyword of dump image. The fixes will pass geometry information about the walls to dump image so that the walls will be included in the rendered image. Please note, that for 2d systems, a wall rendered as a plane would be invisible and it is thus rendered as a cylinder.

The color of the wall is by default that of the first atom type when using color styles “type” or “element”. With color style “const” the default value of “white” can be changed using dump_modify fcolor. The transparency is by default fully opaque and can be changed with dump_modify ftrans.

For 2d systems, the fflag1 setting determines whether the cylinder representing the wall is capped with a sphere at the ends: 0 means no caps, 1 means the lower end is capped, 2 means the upper end is capped, and 3 means both ends are capped. The fflag2 setting allows to adjust the radius of the rendered cylinder. It should be set to a value > 0 or the cylinder will not be visible since the diameter is set internally to zero due to lack of a suitable heuristic for deriving a meaningful diameter for all types of walls and unit settings.

For 3d systems, both fflag1 and fflag2 are ignored.

## Restart, fix_modify, output, run start/stop, minimize info

No information about these fixes are written to binary restart files.

The fix_modify energy option is supported by these fixes to add the energy of interaction between atoms and all the specified walls to the global potential energy of the system as part of thermodynamic output. The default setting for these fixes is fix_modify energy no.

The fix_modify virial option is supported by these fixes to add the contribution due to the interaction between atoms and all the specified walls to both the global pressure and per-atom stress of the system via the compute pressure and compute stress/atom commands. The former can be accessed by thermodynamic output. The default setting for these fixes is fix_modify virial no.

The fix_modify respa option is supported by these fixes. This allows to set at which level of the r-RESPA integrator a fix is adding its forces. Default is the outermost level.

These fixes compute a global scalar energy and a global vector of forces, which can be accessed by various output commands. Note that the scalar energy is the sum of interactions with all defined walls. If you want the energy on a per-wall basis, you need to use multiple fix wall commands. The length of the vector is equal to the number of walls defined by the fix. Each vector value is the normal force on a specific wall. Note that an outward force on a wall will be a negative value for lo walls and a positive value for hi walls. The scalar and vector values calculated by this fix are “extensive”.

No parameter of these fixes can be used with the start/stop keywords of the run command.

The forces due to these fixes are imposed during an energy minimization, invoked by the minimize command.

Note

If you want the atom/wall interaction energy to be included in the total potential energy of the system (the quantity being minimized), you MUST enable the fix_modify energy option for this fix.

Styles with a gpu, intel, kk, omp, or opt suffix are functionally the same as the corresponding style without the suffix. They have been optimized to run faster, depending on your available hardware, as discussed on the Accelerator packages page. The accelerated styles take the same arguments and should produce the same results, except for round-off and precision issues.

These accelerated styles are part of the GPU, INTEL, KOKKOS, OPENMP, and OPT packages, respectively. They are only enabled if LAMMPS was built with those packages. See the Build package page for more info.

You can specify the accelerated styles explicitly in your input script by including their suffix, or you can use the -suffix command-line switch when you invoke LAMMPS, or you can use the suffix command in your input script.

See the Accelerator packages page for more instructions on how to use the accelerated styles effectively.

## Restrictions

Fix wall/lepton is part of the LEPTON package and only enabled if LAMMPS was built with this package. See the Build package page for more info.

## Related commands

fix wall/reflect, fix wall/gran, fix wall/region

## Default

The option defaults units = lattice, fld = no, and pbc = no.

(Magda) Magda, Tirrell, Davis, J Chem Phys, 83, 1888-1901 (1985); erratum in JCP 84, 2901 (1986).

(Barraud) Barraud, Dalmazzone, Moureta, De Bruin, Creton, Pasquier, Lachet and Nieto-Draghi, Langmuir, 41 (11), 7272-7282 (2025).