You might want to try something like:

ClearAll["Global`*"]

Manipulate[
 Grid[
  {{
    Plot[\[Phi][x, c0, \[Phi]2, x2], {x, 0, 10},
     PlotRange -> {0, 0.3},
     FrameLabel -> {Row[{Style["x", Italic], "[nm]"}],
       Row[{Style["Potential", Italic], "(mV)"}]},
     PlotLabel -> Row[{"Potential profile of a monovalent salt"}],
     PlotStyle -> {Thick, Blue},
     Frame -> True,
     PerformanceGoal -> "Quality",
     ImageSize -> 280
     ],
    Plot[cf[x, c0, \[Phi]2, x2], {x, 0, 0.5},
     PlotRange -> All,
     FrameLabel -> {Row[{Style["x", Italic], "[nm]"}],
       Row[{Style["Concentration", Italic], "(M)"}]},
     PlotLabel -> 
      Row[{"Concentration profile of a monovalent salt"}],
     PlotStyle -> {Thick, Green},
     Frame -> True,
     PerformanceGoal -> "Quality",
     ImageSize -> 280
     ],
    Plot[cd[0.8, c0, \[Phi]2, x2], {x2, -200, 200},
     PlotRange -> {0, All},
     FrameLabel -> {Row[{Style["\[Phi]", Italic], "[mV]"}],
       Row[{Style["Capacitance", Italic], 
         "(\!\(\*FractionBox[\(\[Micro]F\), SuperscriptBox[\(cm\), \
\(2\)]]\))"}]},
     PlotLabel -> Row[{"Stern model"}],
     PlotStyle -> {Thick, Red},
     Frame -> True,
     PerformanceGoal -> "Quality",
     ImageSize -> 280
     ]
    }}
  ],
 {{c0, 0.15, "Initial concentration (M)"}, 0, 1, 
  Appearance -> "Labeled"},
 {{x2, 0, "x2 (nm)"}, 0, 2, Appearance -> "Labeled"},
 {{\[Phi]2, 200, "\[Phi]2 (mV)"}, 0, 250, Appearance -> "Labeled"},
 Initialization :> (
   z = 1;
   T = 300; 
   \[Epsilon]0 = 8.854*10^-12;
   \[Epsilon] = 80;
   R = 8.314;
   F = 96485.33;
   xmax = 20;

   \[Kappa][
     c0_] := (((2*(c0*1000)*F^2)/(\[Epsilon]*\[Epsilon]0*R*T))^(
      1/2)*10^-9);
   \[Phi][x_, c0_, \[Phi]2_, x2_] := \[Phi]2*
     Exp[-\[Kappa][c0]*(x - x2)];
   cf[x_, c0_, \[Phi]2_, x2_] := 
    c0*Exp[-z*F*\[Phi][x, c0, \[Phi]2, x2]/(1000*R*T)];
   cd[x_, c0_ , \[Phi]2_, 
     x2_] := ((x2*10^-11)/(\[Epsilon]*\[Epsilon]0) + (
      1*10^-11)/(\[Epsilon]*\[Epsilon]0*\[Kappa][c0]*
       Cosh[(z*F*\[Phi][x, c0, \[Phi]2, x2])/(2*1000*R*T)]))^-1;
   )
 ]

The $\kappa$ in the definition of cd had no argument and the third plot did not vary or give a value for x - the first input to the function cd.

Cheers,

Marco

Vanessa,

For ParametricPlot to work $\phi$ cannot simultaneously be a dependent and independent variable. If you let $x$ be the independent variable, you can obtain a ParametricPlot.

Manipulate[
 Grid[
  {{
    Plot[\[Phi][x, c0, \[Phi]2, x2], {x, 0, 10},
     PlotRange -> {0, 0.3},
     FrameLabel -> {Row[{Style["x", Italic], "[nm]"}],
       Row[{Style["Potential", Italic], "(mV)"}]},
     PlotLabel -> Row[{"Potential profile of a monovalent salt"}],
     PlotStyle -> {Thick, Blue},
     Frame -> True,
     PerformanceGoal -> "Quality",
     ImageSize -> 280
     ],
    Plot[cf[x, c0, \[Phi]2, x2], {x, 0, 0.5},
     PlotRange -> All,
     FrameLabel -> {Row[{Style["x", Italic], "[nm]"}],
       Row[{Style["Concentration", Italic], "(M)"}]},
     PlotLabel -> Row[{"Concentration profile of a monovalent salt"}],
     PlotStyle -> {Thick, Green},
     Frame -> True,
     PerformanceGoal -> "Quality",
     ImageSize -> 280
     ],
    ParametricPlot[{\[Phi][x, c0, \[Phi]2, x2], 
      cd[x, c0, \[Phi]2, x2]}, {x, 0, 10},
     FrameLabel -> {Row[{Style["\[Phi]", Italic], "[mV]"}],
       Row[{Style["Capacitance", Italic], 
         "(\!\(\*FractionBox[\(\[Micro]F\), SuperscriptBox[\(cm\), \
\(2\)]]\))"}]},
     PlotLabel -> Row[{"Stern model"}],
     PlotStyle -> {Thick, Red},
     Frame -> True,
     PerformanceGoal -> "Quality",
     ImageSize -> 280
     ]
    }}
  ],
 {{c0, 0.15, "Initial concentration (M)"}, 0, 1, 
  Appearance -> "Labeled"},
 {{x2, 0, "x2 (nm)"}, 0, 2, Appearance -> "Labeled"},
 {{\[Phi]2, 200, "\[Phi]2 (mV)"}, 0, 250, Appearance -> "Labeled"},
 Initialization :> (
   z = 1;
   T = 300; 
   \[Epsilon]0 = 8.854*10^-12;
   \[Epsilon] = 80;
   R = 8.314;
   F = 96485.33;
   xmax = 20;

   \[Kappa][
     c0_] := (((2*(c0*1000)*F^2)/(\[Epsilon]*\[Epsilon]0*R*T))^(
      1/2)*10^-9);
   \[Phi][x_, c0_, \[Phi]2_, x2_] := \[Phi]2*
     Exp[-\[Kappa][c0]*(x - x2)];
   cf[x_, c0_, \[Phi]2_, x2_] := 
    c0*Exp[-z*F*\[Phi][x, c0, \[Phi]2, x2]/(1000*R*T)];
   cd[x_, c0_, \[Phi]2_, 
     x2_] := ((x2*10^-11)/(\[Epsilon]*\[Epsilon]0) + (
      1*10^-11)/(\[Epsilon]*\[Epsilon]0*\[Kappa][c0]*
       Cosh[(z*F*\[Phi][x, c0, \[Phi]2, x2])/(2*1000*R*T)]))^-1;
   )
 ]