PowerShell: Create a SharePoint Application Pool (http://blogs.technet.com/b/fromthefield/archive/2014/03/26/create-a-sharepoint-application-pool-using-powershell.aspx)

New-SPApplicationPool.ps1

asnp *SharePoint* -ErrorAction SilentlyContinue

// URL of the Web App to change the Application Pool of.
$WebAppURL = "http://WebApp"

// name of the name Application Pool that will be created.
$NewAppPoolName = "NewAppPool"

//the user account that the Application Pool will run under the context of.
$NewAppPoolUserName = "contoso\apppool"

/* All done. Go time. */
$Farm = Get-SPFarm
$Service = $Farm.Services | where {$_.TypeName -eq "Microsoft SharePoint Foundation Web Application"}
$Password = Read-Host -Prompt "Please enter your password" -AsSecureString
$NewAppPool = New-Object Microsoft.SharePoint.Administration.SPApplicationPool($NewAppPoolName,$Service)
$NewAppPool.CurrentIdentityType = "SpecificUser"
$NewAppPool.Username = $NewAppPoolUserName
$NewAppPool.SetPassword($Password)
$NewAppPool.Provision()
$NewAppPool.Update($true)

$NewAppPool = $Service.ApplicationPools[$NewAppPoolName]
$WebApp = Get-SPWebApplication $WebAppURL
$WAAppPool = $WebApp.ApplicationPool = $NewAppPool
$WebApp.Update()
$WebApp.ProvisionGlobally()